Graphene is a one-atom thick layer of crystalline carbon that was first isolated in 2004 by University of Manchester scientists, Andre Geim and Kostya Novoselov. Graphene is different from other materials in that its charge-carrying electrons move at extremely high speeds, behaving like relativistic particles with no rest mass. As a result graphene has all sorts of unusual properties, including the highest room temperature conductivity of any known material, extremely high sensitivity to chemicals (it can sniff out a single molecule) and optical properties that allow it to go from being transparent to opaque when a voltage is applied.

Physicists have predicted that the relativistic charge carriers in graphene are correlated – that is, they interact strongly with each other. "Such correlations often lead to unexpected collective phenomena, where the whole is more than the sum of the parts, and fundamentally new properties," explains team leader Eva Andrei at Rutgers University. "Examples of such collective effects include superconductivity, magnetism and superfluidity."

Can relativistic particles be correlated?
Before graphene was discovered, it was difficult to observe correlations in relativistic particles. For example, collective phenomena cannot be observed in neutrinos, which come from the Sun or are produced in high-energy colliders, because they are too sparse – at least here on Earth, says Andrei. Some researchers even believe that correlations might not occur at all in these particles.

Now, Andrei's team has confirmed that charge carriers in graphene do interact strongly with each other and show collective behaviour that can be detected as the fractional quantum Hall effect (FQHE). This effect occurs when charge carriers like electrons are confined to moving in a 2D plane, as in graphene, and subjected to a perpendicular magnetic field. The charge carriers then form new quasiparticles with a fraction of the charge on an elementary electron.

The FQHE is fundamentally different from the integer quantum Hall effect and forms thanks to strong interactions between electrons. In this state, the electrons and flux lines from the magnetic field form a coherent "liquid" of composite particles each consisting of an electron and an even number of captured flux lines.

Fractional statistics
"The FQHE represents an entire family of quantum phases, the most robust of which is the 1/3 FQHE described as two flux lines captured by each electron," said Andrei. "These fractionally charged quasiparticles obey so-called fractional statistics, a feature that may be important for developing future quantum computers."

The researchers obtained their results by first depositing a graphene flake on a standard semiconductor wafer consisting of a silicon crystal capped with a thin silica layer. The flake was produced by rubbing graphite on the wafer – the same process that occurs when you write with a pencil. Andrei's team then used scanning electron lithography and thin film deposition to define electrical contacts made of gold and titanium on the flake.

The next step was to expose the sample to a strong acid that etched away the silica but which did not affect the graphene, electrodes or silicon, to produce a graphene strip suspended in air. Finally, the sample was cleaned by heating it to very high temperatures to "boil off" any impurities that may have landed on it during fabrication.

Cleanliness the key to success
The FQHE is detected by measuring the resistance of graphene (cooled to about 2K and in an applied magnetic field) as a function of applied voltage. The appearance of "plateaus" in the resistance – which become more pronounced as the field increases – revealed the FQHE state.

"Suspending and cleaning graphene were crucial steps that isolated it from its environment and removed impurities," said Andrei. "They allowed the electrons to interact with each other rather than with other charges and impurities in their surroundings, as in previous work."

The researchers also had the bright idea of using an unconventional non-invasive two-terminal lead geometry to probe the FQHE. This configuration minimizes interference between the electrodes and the measurement process while allowing the graphene to remain mechanically stable. "We will describe our two-terminal measurement technique and how it allows us to access the Hall effect in mesoscopic-sized samples in a forthcoming publication," revealed Andrei.

By demonstrating that relativistic particles do interact strongly, our work implies that new phases of matter will emerge that have unexpected collective properties very different to conventional materials with non-relativistic charge carriers, she added.

The work is reported in Nature.